Target Defense Using a Turret and Mobile Defender Team

A scenario is considered wherein a stationary, turn constrained agent (Turret) and a mobile agent (Defender) cooperate to protect the former from an adversarial mobile agent (Attacker). The Attacker wishes to reach the Turret prior to getting captured by either the Defender or Turret, if possible. Meanwhile, the Defender and Turret seek to capture the Attacker as far from the Turret as possible. This scenario is formulated as a differential game and solved using a geometric approach. Necessary and sufficient conditions for the Turret-Defender team winning and the Attacker winning are given. In the case of the Turret-Defender team winning equilibrium strategies for the min max terminal distance of the Attacker to the Turret are given. Three cases arise corresponding to solo capture by the Defender, solo capture by the Turret, and capture simultaneously by both Turret and Defender.